Issue 37

Z. Hongping et alii, Frattura ed Integrità Strutturale, 37 (2016) 352-359; DOI: 10.3221/IGF-ESIS.37.46 356 of random variable relating to resistance and loading are all considered during the time period. Hence the maximum value of probability in the reference time period can be taken as the value of load. The practical conditions of P (t) and S (t) are shown in Fig. 1. P (t) , S (t) P (t) S (t) Figure 1. Changes of resistance and load. From the perspective the concept of time-dependent reliability, P is a time-dependent function. But in time comprehensive analysis method, P is considered as a definite value and also the maximum value in the whole reference time period. It should be pointed out that, definite value herein does not refer to determined value, but random variable. We can obtain the practical value of P from probability density function fp. In time comprehensive analysis method, failure probability can be obtained using the following formula.   min max ( ) f A D t D P S   (15) max 0 max ( ) t t A S S t    represents for the maximum load effect in the whole evaluation reference period [0, T] and min 0 min ( ) t t A P P t    represents for the maximum resistance in different stages in the whole evaluation reference period [0, T]. In practical application of time comprehensive analysis method, probability density function of ( ) S t can be obtained through long- term observation of data. In this way, max S can be obtained probability distribution function. But it is a pity that, long-term observation data are difficult to be obtained. Therefore, the extreme value distribution can be described by some short-term data. time-dependent reliability can be calculated by first order reliability method after analysis of load and resistance rules of structural element. Analysis of time-dependent reliability of corroded bending element A flexural simply supported beam component of reinforced concrete in someplace was taken as an example. Beam span was 6000 mm, spacing was 3,900 mm, and section size was 250 mm × 500 mm. The thickness of concrete cover was 25 mm, concrete strength was C20, and grade II rebar with a diameter of 16 mm was used, with a reinforcement ratio of 1.2%. As to the external environment, relative humidity was 71% and temperature was 13 o C; besides, 2 co k was 1.2 and ce k was 2.0. We know that, the reinforcement began to be corroded 13.7 years ago and the concrete cover began to crack due to corrosion expansion 26.5 years ago, after substituting relevant coefficients according the method stated in literature [16]. Other relevant resistance statistical parameters were as follows: K r  = 1.0, K r  = 0.04; l  = 1.0l, l  = 0.02; b  = 1.0b, b  = 0.03. The simply supported beam bears constant load and live load. The average value and standard error of constant load, i.e., G  and G  , were 28.91 KN/m and 2.03 KN/m respectively. The average value and standard error of live load, i.e., Q  and Q  , were 0.585 KN/m and 0.26 KN/m. The relevant parameters were substituted into the resistance decrease model of corroded bending element of reinforced concrete, and then the curve for time-dependent variation of average value and variation coefficient of resistance could be obtained (Fig. 2 and 3). According to Unified Standards for the Design of Reliability of Building Structure (GB50068-2001), the constant load followed normal distribution; the live load followed the I-type distribution of extreme value and the maximum value in the time interval [0, T] also followed I-type distribution of extreme value. The average value and standard error of live load can be obtained using the following formulas.